The wireless communications industry has grown exponentially in recent years. In any wireless communications system, the radio frequency (RF) transmitter plays an important role. The power amplifier (PA) for an RF transmitter is the last stage of amplification in the transmitter chain. The performance of the PA for a wireless transmitter is critical and challenging in the transmission path for a wireless system. Since the PA is designed to drive large power into a load, such as an antenna, by a supply circuit, it is power-hungry and dominates the power dissipation of the transceiver unit. Further, since the PA is a critical element of the transmission path, it is expected to provide the desired output power with designed gains, high efficiency and linearity. New technologies have been developed to improve the efficiency of the PA. One of the key techniques is to use envelope tracking (ET) to provide supply voltage for the PA. An envelope tracking system constantly adjusts the supply voltage to the PA according to the input signal such that the power amplifier is operating more efficiently. Moreover, predistortion is often employed to mitigate AM/PM effect and further improve PA's linearity performance. For example, the digital predistortion, including an AM/AM predistortion and/or an AM/PM distortion, is used to improve system linearity. The problem occurs when the PA characteristics changes over time. PA characteristics are known to vary with circuitry or environmental factors such as load mismatch, temperature shift, voltage standing wave ratio (VSWR) changes, device aging and so on. Changes in PA characteristics result in loss of linearity and efficiency. One way to combat the problem is using open-loop calibration. However, open-loop calibration requires prior information about PA characteristics, which requires long factory calibration time due to the complexity of characterizing all combinations of different factors described above. Closed-loop adaptive calibration is preferred to track changes in PA characteristics. The challenges for closed-loop calibration are how to track the changes of PA characteristics adaptively and efficiently. Further, with the PA-related changes in the system, such as circuitry changes or environmental factors, setting a new PA target response is required or preferred to improve the overall system performance.